My understanding is that they typically do, you book your own ticket for and they put you on a plane, even later the same day if you want. They'll only keep you

My understanding is that they typically do, you book your own ticket for and they put you on a plane, even later the same day if you want. They'll only keep you in detention if you're trying to fight the deportation and have to wait for a hearing, or if you have no way to pay for a ticket -- then they find a low-cost ticket some time out and hold you until then.